Sprawdzanie dokładności szacowania wartości oczekiwanej metodą Monte Carlo

Przedmiotem badań jest estymator wartości oczekiwanej. Sprawdzano dokładność estymacji wartości oczekiwanej w sytuacji, gdy estymator obliczany jest na podstawie danych z rozkładu Gaussa. Sprawdzanie dokładności estymacji wykonano z zastosowaniem metody Monte Carlo.

The subject of the research is the mean value estimator. The estimator is determined based on data obtained from a Gaussian distribution. The accuracy of the mean value estimator was examined using the Monte Carlo method. Chapter 1 provides basic information on the reasons for use the Monte Carlo method. In Chapter 2 the basic definitions were presented. Eq. (1) describes the expected value of the random variable. Eq. (3) presents the mean value estimator. Eq. (4) it is the error of the estimator (3). In the next part of Chapter 2 the mean value estimator for Gaussian distribution was presented (eq. 6). Eq. (7) describes the error of the mean value estimator (6). Next equation describes coverage factor for Gaussian distribution. In the next part of the paper the Monte Carlo methods were presented. In this article the Crude and Hit-or-Miss Monte Carlo methods have been used. Eq. (13) presents the mean value estimator obtained using the Crude Monte Carlo method. Eq. (14) describes the error of the estimator. Eq. (15) presents the mean value estimator obtained using the Hit-or-Miss Monte Carlo method. Eq. (16) it is the error of the estimator. In Fig. 1 the errors (4), (14) and (16) have been shown. Tab. 1 presents the errors obtained in Matlab, MatCAD and LabWINDOWS. The researches have been summarized in Chapter 3.